Rapid mixing of subset Glauber dynamics on graphs of bounded tree-width
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Sparse reliable graph backbones
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Approximating the statistics of various properties in randomly weighted graphs
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Approximating the partition function of the ferromagnetic Potts model
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On the k-edge-incident subgraph problem and its variants
Discrete Applied Mathematics
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The Tutte‐Gröthendieck polynomial T(G; x, y) of a graph G encodes numerous interesting combinatorial quantities associated with the graph. Its evaluation in various points in the (x, y) plane give the number of spanning forests of the graph, the number of its strongly connected orientations, the number of its proper k‐colorings, the (all terminal) reliability probability of the graph, and various other invariants the exact computation of each of which is well known to be #P‐hard. Here we develop a general technique that supplies fully polynomial randomised approximation schemes for approximating the value of T(G; x, y) for any dense graph G, that is, any graph on n vertices whose minimum. © 1995 Wiley Periodicals, Inc.